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Optical Frequency Combs: Nonlinear Optics and the Meeting of the Ultrafast and Ultrastable Scott Diddams National Institute of Standards and Technology Dept. of Physics University of Colorado Boulder, CO [email protected] 1 Learning & Research: A continuous upward climb Chopicalqui (6354m), Peru Bramante Staircase, Vatican 2 Outline 1. Background: Clocks and Precise Timing 2. Counting Cycles of Light • The optical frequency comb 3. From Lab Scale to Chip Scale • Can we make a frequency comb on a chip? 4. Applications and opportunities for frequency combs 3 Boulder Colorado 25 square miles surrounded by reality • Population of ~100k • 30 min from Denver (1.5 M) • Federal Researh Labs: NIST, NOAA, NCAR (atmospheric research) • Home of University of Colorado • Many high-tech companies and startups 4 Boulder Colorado 25 square miles surrounded by reality 5 Boulder Colorado 25 square miles surrounded by reality 6 National Institute of Standards & Technology (NIST) NIST’s mission is to promote U.S. innovation… Key roles enabling innovation, education, and infrastructure for investments in the future… NIST Boulder assets include (approximate values): • 375 employees. • 350 associates. • Postdocs, grad & undergrad students, contractors, guest researchers, etc. • $100 million annual operating budget. • Appropriations, other agency reimbursements. • About 20% of NIST Laboratory programs overall. Research at NIST Boulder Chem-Physics Electromagnetics Nanotechnology Quantum Information Atomic Clocks Lasers/Photonics Advanced Materials Time and Frequency Metrology Cs Fountain Clock Chip-Scale Clocks Single Ion Clocks Optical lattice clocks Optical Frequency Combs Background: Clocks and Precise Timing Salvador Dali: The persistence of memory (1931) 10 10-18 10-12 Still shorter: Top Quark lifetime: 4x10-25 s Planck time: 10-43 s 10-4 100 Time (s) 104 108 1012 Age of universe Human evolution Earth around sun Rotation of earth Heartbeat 10-8 Camera flash Computer clock cycle Chemistry Shortest human-made event Bohr orbital Timescales Human Experience 1018 What Makes a Clock? Oscillator + Earth Rotation Pendulum Quartz Crystal ATOMIC CLOCKS Microwave Transition + Oscillator Optical Transition + Laser Counting Mechanism Sundial Clock Gears/Hands Electronic Counter Electronic Counter Femtosecond Laser Jan. 21, 1945 First public description of atomic clocks given at 1945 APS/AAPT meeting and recorded by the New York Times….. Cs Fountain Clock: The Current Standard and the Definition of the Second fCs=9,192,631,770 Hz Total Uncertainty ~1×10-16 Cold Atoms allow long interaction times S. Jefferts, T. Heavner, T. Parker (NIST) Optical Atomic Clocks Atom(s) Detector & Slow Laser Control Laser Fast Laser Control Isolated Optical Cavity νo Δν At NIST/JILA: Ca, Hg+, Al+, Yb, Sr Atomic Resonance Counter & Read Out (laser frequency comb) •Isolated cavity narrows laser linewidth and provides short term timing reference •Atoms provide long-term stability and accuracy— now now at 10-18 level! •Laser frequency comb acts as a divider/counter Types of Clocks “Better” Loses 1 sec. in: Size: Stability (1s): Cost: Optical Clock Primary Standard Compact Atomic Clock 1010 yrs laboratory 10-16 ?? 108 yrs 107 cm3 10-13 $1 M 1000 yrs 100 cm3 10-10 $1,000 Precision Wristwatch Quartz Crystal Quartz Crystal 1 yr 1 cm3 10-11 $100 1 day 10-3 cm3 10-6 $1 “Smaller” All atomic clocks have: •Reference atom •Local oscillator (pendulum) •Counter/gears Figure: J. Kitching, (NIST) Timekeeping: The long view Oscillator Freq. f = 1 Hz Rate of improvement since 1950: 1.2 decades / 10 years f = 10 kHz f = 10 GHz f = 500 THz Gravitational red shift of 10 cm Sr optical clock ? f = 10-100 PHz ?? S. Diddams, et al, Science (2004) Moore’s Law for Transistors per Chip Rate of growth since 1970: 1.5 decades / 10 years Wiki: "Transistor Count and Moore's Law ” Timekeeping: Societal and Scientific Impact Oscillator Freq. f = 1 Hz f = 10 kHz f = 10 GHz f = 500 THz Gravitational red shift of 10 cm Sr optical clock ? f = 10-100 PHz ?? S. Diddams, et al, Science (2004) Nobel Prizes Related to Timekeeping 1943 Otto Stern Molecular/atomic beam spectroscopy. 1944 Isidor Rabi Atomic beam resonance technique. 1955 Polykarp Kusch Magnetic moment of electron; early atomic clocks. 1964 Charles Townes, Nicolai Basov, Alexandr Prokhorov Quantum electronics, including maser/laser principles. 1966 Alfred Kastler Optical pumping methods. 1989 Norman Ramsey, Hans Dehmelt, Wolfgang Paul Atomic clock techniques; trapped ion spectroscopy. 1997 Bill Phillips, Steven Chu, Claude Cohen-Tannoudji Laser cooling of neutral atoms. 2001 Eric Cornell, Carl Wieman, Wolfgang Ketterle Bose-Einstein condensate. 2005 Jan Hall, Ted Hansch, Roy Glauber Femtosecond laser frequency combs. 2012 Dave Wineland, Serge Haroche Quantum state measurement and manipulation. Bill Phillips NIST Carl Wieman JILA/CU Eric Cornell JILA/NIST Jan Hall JILA/NIST Dave Wineland NIST Splitting the Second, Tony Jones Why do we need better clocks? • Time/Frequency are best known physical quantities: The anchor of the SI (the Second impacts Length, Mass, Voltage, Current…) • Navigation and communication • Geodesy: Gravitational red shift of 1 cm in earth’s potential ~ 1x10-18 • Probe for “New” Physics: - Constancy of fundamental constants - Local position invariance - Tests of QED - Astrophysics – millisecond pulsars • Quantum state engineering: In the future the best clocks will employ quantum entanglement Outline 1. Background: Clocks and Precise Timing 2. Counting Cycles of Light • The optical frequency comb 3. From Lab Scale to Chip Scale • Can we make a frequency comb on a chip? 4. Applications and opportunities for frequency combs 22 Counting Cycles of Light 23 How Do You Count Optical Cycles? Optical Frequency: c/600 nm = 500 THz à T=2 fs Fastest electronics: 1 THz, 1 ps Optical Heterodyne: Measure “beat note” between two optical frequencies Carrier: (f1 + f2)/2 Envelope: (f1 - f2) f1 f2 500,000,010,000,000 Hz - 500,000,000,000,000 Hz 10,000,000 Hz A countable frequency! But only a relative one 24 Direct Multiplication noptical nmicrowave » 1015 1010 » 105 » 216 It worked! But not general, practical, cost effective NIST ~1983 Frequency Chain Laboratory (100 m2) NBS Laser Frequency Synthesis Chain (1979) K. M. Evenson, D. A. Jennings, J. S. Wells, C. R. Pollock, F. R. Petersen, R. E. Drullinger, E. C. Beaty, J. L. Hall, H. P. Layer, B. L. Danielson, G. W. Day, R. L. Barger 25 What is a laser frequency comb?? http://www.hairmax.com/ Client's quote : "I used to have only one or two good hair days a month. Now, every day is a good hair day." 26 Multiple faces of a frequency comb 1. A ruler for light frequencies Hz Intensity fr Dn Frequency 2. A perfectly-spaced train of optical pulses 1 Dn 1 fr Time 27 Multiple faces of a frequency comb 3. An optical clockwork Frequency Comb n1 • Comb uncertainty at the 20th decimal place • Measurement of optical ratios (e.g. n1 : n2) µ-wave Cs, Rb, etc. n2 • Direct connection from optical to microwave domains 28 Mode-Locked Laser: Basis of the Frequency Comb Time domain E(t) Df 2Df Key Concept: Direct link between optical and microwave frequencies t tr.t = 1/fr Frequency domain I(f) 0 fo Df =2pfo/fr ν n = nfr + fo fr n ~10 5 f Hänsch & Hall, Nobel Lectures 29 Group and phase velocity in modelocked lasers High Reflector Laser Cavity Output Coupler animation from Steve Cundiff Free Space Direct Measurement of Carrier Envelope Phase Shift Input Second order cross-correlation 2 photon detector 2 µm thick pellicle beam splitter Vacuum (300mTorr) Jones et al (2000) 20 ns delay arm (2 cavity lengths) Variable delay for scan •Correlation of pulse i and pulse i+2 •Matched number of bounces Direct Measurement of Carrier Envelope Phase Shift Df Df =2pfo/fr Fix fo/fr And measure Df From interferometric autocorrelation Jones et al (2000) Fit of correlation envelope The femtosecond mode-locked laser comb Femtosecond Laser Frequency Comb f Pulsed output of femtosecond laser mode N + 1 mode N L Laser Cavity → Cavity modes are locked in phase to generate a short pulse once every roundtrip time 2L/vg How does it work? à All femtosecond lasers require: • Laser cavity + broadband gain source and optical components • Dispersion control à b(w) • Power-dependent gain or loss à n2I(r) • Phase modulation à n2I(t) ideal mode spacing: Ideal cavity modes L c 2L real “cold” cavity modes f à Due to dispersion, the cavity modes are not evenly spaced à However, the nonlinear phase-modulation in a mode-locked laser provides the required synchronization of the modes. à Yields a strictly uniform mode comb with spacing vg/(2L) à b2(w) and all higher orders of dispersion are compensated! à Multiple faces of a frequency comb 3. An optical clockwork Frequency Comb n1 • Comb uncertainty at the 20th decimal place • Measurement of optical µ-wave Cs, Rb, etc. ratios (e.g. n1 : n2) n2 • Direct connection from optical to microwave domains 35 Synthesis with an optical frequency comb Optical Synthesizer Optical (nopt) or Microwave (fr , fo ) Reference I(f) µ-wave out fo optical out fr 0 Optical Reference k" fk = ν opt − fb + #ν opt − fb − fo $% no k = n − no = 0, ±1, ±2.... and "#ν opt − fb − fo $% fr = no fk f Microwave Reference ν k = kfr + fo k = 1, 2, 3... Verified to the 20th decimal place! L.S. Ma, et al., Science (2004). 36 Controlling the femtosecond laser comb For most applications with the femtosecond laser frequency comb, we need to measure and control the two degrees of freedom of the frequency comb: fo (offset frequency) and fr (repetition rate) fn = nfr + fo • fo measured by “self-referencing” ØNeed an very broad spectrum (i.e. an octave) • fr controlled with a microwave source or a CW laser • n determined by lower resolution measurement or a combination of measurements 37 The laser comb and its control Operational Definition: Comb = Frequency-stabilized Mode-locked Laser f fr-1 = N / νo fo Δφ = 2π f r Pulsed output fo νn = nfr + fo x2 mode N +1 mode N locked in phase CW laser νο t Operation is fully reversible: Can lock at microwave and synthesize optical T. W. Hänsch and J. Hall, Nobel Lectures; D. J. Jones, et al., Science 288, 635 (2000); S. Diddams, Th. Udem, et al., Science 293, 825 (2001) 38 Measuring/controlling the offset frequency: self-referencing I(f) Jones, et al. Science 288, 635 (2000) f0 fr f 0 fn = nfr + f0 f2n = 2nfr + f0 x2 f0 • f0 is generated from a heterodyne beat between the second harmonic of a group of modes around the nth mode and another group of modes around the 2nth mode. •Main Requirement: A very broad spectrum ØAlternative schemes do exist, for which less than one octave is required: see H. Telle et al. Appl. Phys. B 69, 327 (1999) 39 Getting an octave (or significant portion thereof) two routes…. 1. Start with “narrowband” femtosecond laser and use nonlinear broadening • Advantages •Nonlinear broadening in microstructured or other nonlinear (NL) fibers is now straightforward •Can produce octaves about various center wavelengths •HNLF for 1.5 microns provides fully-spliced and robust system. • Disadvantages •Free-space coupling to small core, highly nonlinear microstructure fibers is “tweaky” and challenging to use for long-term operation (>a few hours) •Excess noise can be generated in NL fibers, which in some cases can completely erase the comb structure 2. Generate very broadband spectra directly from the laser • Advantages •No excess fiber noise, no “tweaky” fibers • Disadvantages •Challenging laser to construct (although it is getting easier) •Thus far, only works with Ti:sapphire (~550-1200 nm) 40 Microstructure optical fiber continuum generation CLEO Postdeadline (CPD8) Baltimore (1999). J. Ranka, R. Windeler, A. Stentz, Opt. Lett. 25, 25 (2000). •Tight confinement of light leads to high nonlinearity and ~20 microns anomalous dispersion in the wavelength regime of femtosecond Ti:sapphire lasers •Such fibers are available from commercial sources (ThorLabs, Crystal Fibre) and are developed in research labs (OFS, Univ. of Bath) 41 Octave-Span Supercontinuum 1 GHz Ti:sapphire 100 MHz Er:fiber OC 532 nm PUMP also…. Yb:fiber Yb:crystalline Tm:fiber ….. S. Diddams, JOSA B (2010) A. Bartels, H Kurz, Opt. Lett. 27, 1839 (2002) L. E. Nelson et al., APB 65, (1997) Nonlinear interferometer for measuring f0 Nonlinear Fiber fs Laser Infrared Visible KNbO3 For SHG fo fr - fo Polarizer Filter f0 Other interferometer designs exist: • inline with waveguide PPLN • Michelson 43 GHz Rep Rate Ti:Sapphire Combs T. Fortier, A. Bartels, D. Heinecke, M. Kirchner M3 1 GHz Octave Spanning Laser OC PUMP M1 M2 10 GHz Self-referenced Ti:sapphire Laser Yb CaSr Al+ Hg+ A. Bartels, H Kurz, Opt. Lett. 27, 1839 (2002) T. Fortier, A. Bartels, S. Diddams, CLEO (2005) T. Fortier, A. Bartels, S. Diddams, Opt. Lett. 31, 1011 (2006) • • • Stabilized Comb = 106 Modes Hz-level linewidths Residual frequency noise at 1×10-19 level A. Bartels, D. Heinecke, S. Diddams, Science 326, 681 (2009). 44 Er:fiber based frequency combs à mode-locking based on nonlinear polarization rotation Launched polarization state Ultrashort pulse train Nonlinearlyrotated polarization ellipse WDM + Iso. SMF λ/2 λ/4 PBS λ/2 λ/4 SMF 980 nm pump (x2) erbium-doped fiber EDF 45 Polarization-maintaining Er:fiber laser comb • Laser + amplifier + self-referencing are all constructed “in-line” with polarization-maintaining (PM) fiber optics. • Laser is mode-locked with saturable absorber mirror • Robust against environmental perturbations. (Newbury group at NIST) Frequency comb operates phase-locked in a moving vehicle. L. Sinclair, et al. Opt. Express 22, 6996-7006 (2014) 46 High-power Yb:fiber laser frequency comb • Linear cavity design • Saturable absorber end mirror for mode-locking • Fiber Bragg grating provides output coupling and dispersion control • External amplification to ~80 W followed by compression to ~100 femtosecond pulses • Supports sub Hz linewidths Schibli, et al. Nature Photonics 2, 355 - 359 (2008) 47 Frequency Comb Extension via Nonlinear Optics • Using a combination of harmonic generation, difference frequency generation and super-continuum, frequency combs have been extended from the UV to the infrared Difference Frequency Generation and Continuum Harmonic Generation and Continuum Ti:sapphire 100 500 Er:fiber Yb:fiber 1000 1500 2000 10000 wavelength (nm) • Some examples: o o Extreme ultraviolet via harmonic generation: Phys. Rev. Lett. 94, 193201 (2005); Nature 436, 234237 (2005); Science 307, 400 (2005); Mid-infrared comb generation via OPO, DFG and supercontinuum: Opt. Lett. 34, 1330 (2009); Opt. Lett. 37, 1400 (2012); Lett. 39, 2056 (2014); Opt. Lett. 36, 2275-2277 (2011). 48